Some Results on Cumulative Residual Inaccuracy Measure of k-Record Values

What is it about?

This study extends the concept of cumulative residual inaccuracy (CRI)—an information-theoretic measure that quantifies the inaccuracy between two probability models—to the framework of k-record values. In probability theory, record values represent successive extreme observations in a sequence of random variables. The notion of k-record values generalizes this idea by considering not only the maximum observations but also the second, third, and higher-order extremes. By formulating the CRI for such -record structures, the paper broadens the applicability of inaccuracy-based measures to situations where record-type or extreme-value data are of interest. The work establishes mathematical properties, inequalities, and stochastic ordering relations for the proposed measure and provides explicit results for standard probability distributions. These results enhance the theoretical foundations of inaccuracy-based entropy measures and support their use in reliability analysis, risk modeling, and other areas of science and engineering concerned with extremal behavior.

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